Answer:
For Equation 1:
- Domain: [tex]\mathbb{R}[/tex]
- Range: [tex]\mathbb{R}[/tex]
- Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]
- Y-intercept: 6
For Equation 2:
- Domain: [tex]\mathbb{R}[/tex]
- Range: [tex]\mathbb{R}[/tex]
- Slope: [tex]\frac{3}{4}[/tex]
- Y-intercept: -4
Step-by-step explanation:
We are given two lines - one is an equation and one is an inequality.
Neither are in slope-intercept form (y = mx + b), so we need to make these adjustments.
Slope-intercept form has two key parts to the equation: m, which is the slope of the line and b, which is the y-intercept of the line.
Equation 1
[tex]\displaystyle2x+3y=18\\\\3y = -2x + 18\\\\y = -\frac{2}{3}x+6[/tex]
With this, we can now determine the domain, range, slope, and y-intercepts for this line.
For Equation 1, because our equation is in slope-intercept form, we can find the slope and the y-intercept.
Our equation is [tex]y=-\frac{2}{3}x+6[/tex]. Therefore, our m is [tex]-\frac{2}{3}[/tex] and our b is 6.
Because the equation is linear, there is no instance in which the line will not meet an x- or y-value. Therefore, our domain and range is all real numbers, or [tex]\mathbb{R}[/tex].
- Domain: [tex]\mathbb{R}[/tex]
- Range: [tex]\mathbb{R}[/tex]
- Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]
- Y-intercept: 6
Equation 2
[tex]\displaystyle3x-4y>16\\\\-4y>-3x+16\\\\y < \frac{3}{4}x-4[/tex]
Now that we have solved the inequality, we can determine our slope, the domain, and the range of the function.
We can use the same tactic as before - m is our slope and b is our y-intercept. Therefore, [tex]\frac{3}{4}[/tex] is our slope and -4 is our y-intercept.
Because the inequality represents a line, our domain is all real numbers, or [tex]\mathbb{R}[/tex]. If we were to plug in any number for x, y would be true for that value. Therefore, our range is also all real numbers, or [tex]\mathbb{R}[/tex].
- Domain: [tex]\mathbb{R}[/tex]
- Range: [tex]\mathbb{R}[/tex]
- Slope: [tex]\frac{3}{4}[/tex]
- Y-intercept: -4
